Combining the deepest Herschel extragalactic surveys (PEP, GOODS-H, HerMES), and Monte Carlo mock catalogs, we explore the robustness of dust mass estimates based on modeling of broadband spectral energy distributions (SEDs) with two popular approaches: Draine & Li (2007, ApJ, 657, 810; DL07) and a modified blackbody (MBB). We analyze the cause, drivers, and trends of uncertainties and systematics in thorough detail. As long as the observed SED extends to at least 160−200 μm in the rest frame, Mdust can be recovered with a >3σ significance and without the occurrence of systematics. An average offset of a factor ~1.5 exists between DL07- and MBB-based dust masses, based on consistent dust properties. The performance of DL07 modeling turns out to be more robust than that of MBB since relative errors on Mdust are more mildly dependent on the maximum covered rest-frame wavelength and are less scattered. At the depth of the deepest Herschel surveys (in the GOODS-S field), it is possible to retrieve dust masses with a signal-to-noise ratio, S/N ≥ 3 for galaxies on the main sequence of star formation (MS) down to M∗ ~ 1010 [M⊙] up to z ~ 1. At higher redshift (z ≤ 2), the same result is only achieved for objects at the tip of the MS or for those objects lying above the tip owing to sensitivity and wavelength coverage limitations. Molecular gas masses, obtained by converting Mdust through the metallicity-dependent gas-to-dust ratio δGDR, are consistent with those based on the scaling of depletion time, τdep, and on CO sub-mm spectroscopy. Focusing on CO-detected galaxies at z> 1, the δGDR dependence on metallicity is consistent with the local relation, provided that a sufficient SED coverage is available. Once we established that Herschel-only and sub-mm-only estimates of dust masses can be affected by large uncertainties and possibly systematics in some cases, we combined far-IR Herschel data and sub-mm ALMA expected fluxes to study the advantages of a full SED coverage. The uncertainty on Mdust reduces to <30% for more than 85% of Herschel galaxies, thus potentially facilitating a fast statistical study of Mdust,gas for large samples, at least up to z ~ 2.

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